The equation of wave is given by Y = 10⁻²sin 2π(160t - 0.5x + π/4) where x and Y are in m and t in s. The speed of the wave is ________ km h⁻¹. Numerical answer type. Work it out, then open the answer.

Answer: 1152. Y = 10⁻²sin (2π · 160 t - 2π · 0.5 x +): ω = 320π, k = π. v = (ω)/(k) = 320 m/s 320 × 18/5 = 1152 km/h So the answer is 1152 km h⁻¹.

The equation of wave is given by Y = 10⁻²sin 2π(160t - 0.5x + π/4)… | JEE Main 2023 (11 Apr, Shift 1)

Q51JEE Main 2023 · 11 APR · SHIFT 1Easy

Progressive Wave Equation

The equation of wave is given by

$Y = 10^{-2}\sin 2\pi(160t - 0.5x + \pi/4)$

where $x$ and $Y$ are in $\text{m}$ and $t$ in $\text{s}$ . The speed of the wave is ________ $\text{km h}^{-1}$ .

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 1152

$Y = 10^{-2}\sin(2\pi \cdot 160\, t - 2\pi \cdot 0.5\, x + \dots)$ : $\omega = 320\pi$ , $k = \pi$ .
$v = \dfrac{\omega}{k} = 320\text{ m/s}$
$320 \times \dfrac{18}{5} = 1152\text{ km/h}$
So the answer is $1152\text{ km h}^{-1}$ .